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The number of bouncers allowed per over irrespective of the batsmen facing is 1 in ODI's and T20's but two in Test matches . But the current rule change which is yet to be implemented will allow bowlers to bowl two bouncers irrespective of the format of the game.

No. Number bouncers is only per over not per batsman .

Any pitched ball above shoulder is a bouncer. If the ball bounces above the head of the batsman , then the delivery will be called a wide(provided the batsman doesn't touch the ball)

As of 1st October 2012, the number of allowed bouncers per over is 2 for Test Matches, 2 for ODIs (changed from 1), and 1 for Twenty20 Internationals. Each of these is above shoulder height. In addition, any ball above head height is wide. If you bowl too many bouncers in an over (no matter to which batsman), you get warned twice and taken off at the third time.

Note that these are ICC playing conditions. The Laws of Cricket use a slightly different distinction. There, any ball above head height is a no ball (Law 42.6(ii)). The Laws also give the umpire more flexibility (or less guidance, if you will), about calling wides and intervening for dangerous bowling. So if you are playing in a league match or a friendly, check your local playing conditions or clarify the interpretation of the laws.

(There is a subtle difference between these two sets of rules, because you can get stumped off a wide but not off a no ball.)

As per the new rule number of bouncers allowed for an over is 2,and any bowler who bowls more than these he wont be allowed to bowl for the current(ongoing) entire match,the other bowler will replace him and try to complete the over.

Above the shoulder is termed as bouncer,however umpire also decide whether to declare the bouncer as wide or not depending upon the height of the ball,the umpire call the bouncer as wide if it is above the height of head